Vector Algebra - Online Test
Q1. Magnitude of the vector 
is
is
Answer : Option B
Explaination / Solution:
Q2. Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7).
Answer : Option C
Explaination / Solution:
The scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7) is given by : (- 5 – 2 ) i.e. – 7 and (7 – 1 ) i.e. 6. Therefore, the scalar components are – 7 and 6 .,and vector components are - 
Q3.
Find the values of x and y so that the vectors are equal
Answer : Option C
Explaination / Solution:
x = 2, y = 3
Q4. Find the sum of the vectors 
Answer : Option C
Explaination / Solution:
We have:
vectors
vectors
Q5. Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.
Answer : Option D
Explaination / Solution:
Let be a unit vector in XY plane,making angle 300 with positive X axis,so we have the vector as
is the required vector.
is the required vector.
Q6. Find the value of x for which is a unit vector
Answer : Option D
Explaination / Solution:
As x is a unit vector ,
therefore,
therefore,
Q7. Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are 
externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.
externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.
Answer : Option C
Explaination / Solution:
Q8. 
Answer : Option C
Explaination / Solution:
Let
Q9. The scalar product of the vector with a unit vector along the sum of vectors is equal to one. Find the value of.
Answer : Option A
Explaination / Solution:
Let and
Therefore, a unit vector along
is given by:
Also, scalar product of with above unit vector is 1.
Therefore, a unit vector along
is given by:
Also, scalar product of with above unit vector is 1.
Q10. The scalar product of two nonzero vectors is denoted by
Answer : Option A
Explaination / Solution:
The scalar product of two nonzero vectors is denoted by .and is defined by =
